具有可选服务的M/G/1重试反馈排队模型的稳定性

研究具有启动失败、第二阶段可选服务的M/G/1重试排队模型,其中两个阶段服务都具有反馈机制。当服务台启动失败时,顾客返回到重试区域,服务台进入修理阶段。所有顾客必须进行第一阶段基本服务,只有部分顾客进行第二阶段可选服务。首先利用嵌入马尔科夫链的方法给出系统遍历的充分必要条件,然后采用补充变量法得到重试区域队长的平稳分布以及服务台处于忙期的概率等相关的系统性能指标,最后引入广义休假的概念,得到系统的随机分解性质。

Stability of M/G/1 Retrial Feedback Queue with Optional Service

An M/G/1 retrial queue with starting failures and the second optional service was studied.Both stages have feedback mechanisms.When starting failure,the customer returns to the retrial area and the“repair”for the serve commences immediately.All customers must carry out the first essential services,and only some customers have the second optional services.Firstly,the necessary and sufficient condition of the ergodicity for the system was given by the method of embedding Markov chain.Then by the method of supplementary variable technique,the distribution of the orbit length and some performance measures under steady-state condition were obtained.And some numerical analysis results were also given.Finally,the property of stochastic decomposition was verified by introducing the concept of generalized vacation.